A walking path across a park is represented by the equation y= -4x - 6 . A new path will be built perpendicular to this path. The path will intersect at the point (-4 , 10) . Identify the equation that represents the new path .

Answer:y=1/4 x +11Step-by-step explanation:So this is a word problem but it isn't too bad to figure what they want:  They are looking for a line that is perpendicular to y=-4x-6 and goes through (-4,10).So we are looking for an equation whose slope is the opposite reciprocal of the given equation's slope.The given equation has a slope of -4The opposite reciprocal of -4 is 1/4 so that is the slope of our new line.So we know our equation is in the form of y=1/4 x+bNow we are given that this line should go through (-4,10) so plug it in to find b.10=1/4 * (-4)+b10=-1+b11=bSo the equation is y=1/4 x+11